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You and your friend each start a car-washing service. You spend $25 on supplies and charge $10 per car. Your friend spends $55 on supplies and charges $13 per car. How many cars do you have to wash to earn the same amount of money as your friend?
cars
To find out how many cars you both need to wash to earn the same amount of money, we can set up equations for both of you.
1. Your Earnings: You spend $25 on supplies and earn $10 for each car washed.
– Earnings = $10 * number of cars – $25
2. Friend’s Earnings: Your friend spends $55 on supplies and earns $13 for each car washed.
– Earnings = $13 * number of cars – $55
We want to find the number of cars (let’s call it ( x )) where both earnings are equal:
[
10x – 25 = 13x – 55
]
Now, let’s solve for ( x ):
1. Rearranging the equation gives:
[
-25 + 55 = 13x – 10x
]
[
30 = 3x
]
2. Divide both sides by 3:
[
x = 10
]
So, you need to wash 10 cars to earn the same amount of money as your friend!